Question

我有两个维度为numpy和(386, 3, 4)的{{1}}矩阵。我想生成(386, 4, 3)的输出维度。换句话说，我希望以矢量化方式执行以下循环 -

(386, 3, 3)

最好的方法是什么？

Answer 1

matmul也有效：

a = np.random.random((243,3,4))
b = np.random.random((243,4,3))
np.matmul(a,b).shape
# (243, 3, 3)

Answer 2

我们需要保持第一个轴对齐，所以我建议使用np.einsum的方法 -

np.einsum('ijk,ikl->ijl',input1,input2)

运行样本以验证形状 -

In [106]: a = np.random.rand(386, 3, 4)

In [107]: b = np.random.rand(386, 4, 3)

In [108]: np.einsum('ijk,ikl->ijl',a,b).shape
Out[108]: (386, 3, 3)

示例运行以验证较小输入的值 -

In [174]: a = np.random.rand(2, 3, 4)

In [175]: b = np.random.rand(2, 4, 3)

In [176]: output = np.zeros((2,3,3))

In [177]: for i in range(len(a)):
     ...:     output[i] = np.matmul(a[i], b[i])
     ...:     

In [178]: output
Out[178]: 
array([[[ 1.43473795,  0.860279  ,  1.17855877],
        [ 1.91036828,  1.23063125,  1.5319063 ],
        [ 1.06489098,  0.86868941,  0.84986621]],

       [[ 1.07178572,  1.020091  ,  0.63070531],
        [ 1.34033495,  1.26641131,  0.79911685],
        [ 1.68916831,  1.63009854,  1.14612462]]])

In [179]: np.einsum('ijk,ikl->ijl',a,b)
Out[179]: 
array([[[ 1.43473795,  0.860279  ,  1.17855877],
        [ 1.91036828,  1.23063125,  1.5319063 ],
        [ 1.06489098,  0.86868941,  0.84986621]],

       [[ 1.07178572,  1.020091  ,  0.63070531],
        [ 1.34033495,  1.26641131,  0.79911685],
        [ 1.68916831,  1.63009854,  1.14612462]]])

运行示例以验证更大输入的值 -

In [180]: a = np.random.rand(386, 3, 4)

In [181]: b = np.random.rand(386, 4, 3)

In [182]: output = np.zeros((386,3,3))

In [183]: for i in range(len(a)):
     ...:     output[i] = np.matmul(a[i], b[i])
     ...:     

In [184]: np.allclose(np.einsum('ijk,ikl->ijl',a,b), output)
Out[184]: True

3D张量的内部维度的矩阵乘法？

2 个答案: